I am learning about edge states at high magnetic field (Quantum ballistic sample). What I understand so far from it is that at high magnetic field, Landau states arise.

Then (I don't know exactly why?), edge states are formed. To enhance my understanding, can someone help me with these questions:

*Why must the chemical potential cross a Landau level?

*Why is the net current carried solely by these edge states?

(I am only interested in intuition, no derivations)